A differential linear perturbation method for apparent I.P. calculations

Paul Wilkinson, Meng Heng Loke, Kim Frankcombe

3-D induced polarization (I.P.) surveys are widely used in exploration of minerals particularly those that contain conductive minerals sulfides that frequently occur in areas with complex geology. The linear perturbation method is frequently used to calculate the apparent resistivity and I.P. values. This method treats the I.P. effect as a linear change of a base conductivity model. The apparent I.P. value is calculated by dividing the difference in the resistivity potentials between the base and perturbed conductivity models with the base model potential. This can lead to significant numerical roundoff errors if the difference in the potentials is much smaller than the base model potential. This occurs if there is large range variation in the model resistivity values and the arrays used have a large range of geometric factors. The use of double-precision calculations or a complex conductivity model greatly reduces the roundoff errors. However, these methods significantly increases the computer memory needed by more than 70% and the calculation time by more than 50%. A new differential linear perturbation method is proposed that calculates the change in the potentials directly (instead of from the difference between the two potential values) that avoids the roundoff error problems. It increases the computer memory by 3% and calculation time by 9%. It enables the calculation of more accurate apparent I.P. values for finite-element models with millions of nodes using a PC.